{"id":"https://openalex.org/W2985317169","doi":"https://doi.org/10.22331/q-2020-08-28-313","title":"Weak approximate unitary designs and applications to quantum encryption","display_name":"Weak approximate unitary designs and applications to quantum encryption","publication_year":2020,"publication_date":"2020-08-28","ids":{"openalex":"https://openalex.org/W2985317169","doi":"https://doi.org/10.22331/q-2020-08-28-313","mag":"2985317169"},"language":"lv","primary_location":{"id":"doi:10.22331/q-2020-08-28-313","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-08-28-313","pdf_url":"https://quantum-journal.org/papers/q-2020-08-28-313/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2020-08-28-313/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"C\u00e9cilia Lancien","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"C\u00e9cilia Lancien","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulouse & CNRS, Universit\u00e9 Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulouse & CNRS, Universit\u00e9 Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":null,"display_name":"Christian Majenz","orcid":null},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Christian Majenz","raw_affiliation_strings":["QuSoft and Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, the Netherlands"],"affiliations":[{"raw_affiliation_string":"QuSoft and Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, the Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.1821,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.74554295,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"4","issue":null,"first_page":"313","last_page":"313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.40059998631477356,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.40059998631477356,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.08009999990463257,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.07569999992847443,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.6604999899864197},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5059000253677368},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.49079999327659607},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.47769999504089355},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4593000113964081},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.40529999136924744},{"id":"https://openalex.org/keywords/quantum-cryptography","display_name":"Quantum cryptography","score":0.40059998631477356},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.39989998936653137},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.3917999863624573}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.6604999899864197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5597000122070312},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5059000253677368},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.49079999327659607},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.47769999504089355},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4593000113964081},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4235999882221222},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.40529999136924744},{"id":"https://openalex.org/C144901912","wikidata":"https://www.wikidata.org/wiki/Q471906","display_name":"Quantum cryptography","level":4,"score":0.40059998631477356},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.39989998936653137},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3917999863624573},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.38440001010894775},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3668000102043152},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.366100013256073},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.33000001311302185},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.3190000057220459},{"id":"https://openalex.org/C95466800","wikidata":"https://www.wikidata.org/wiki/Q1027298","display_name":"Quantum key distribution","level":3,"score":0.3100000023841858},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.30979999899864197},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3050999939441681},{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.3028999865055084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2971999943256378},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.28859999775886536},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28279998898506165},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.28139999508857727},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2793999910354614},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.27000001072883606},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.2531999945640564},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2020-08-28-313","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-08-28-313","pdf_url":"https://quantum-journal.org/papers/q-2020-08-28-313/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1911.06742","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.06742","pdf_url":"https://arxiv.org/pdf/1911.06742","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-03024389v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03024389","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum, 2020, &#x27E8;10.22331/q-2020-08-28-313&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:cwi.nl:30102","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/30102","pdf_url":"https://ir.cwi.nl/pub/30102/30102.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum vol. 4","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:599d93ea3e394e98ac54e6fc38c65ecc","is_oa":true,"landing_page_url":"https://doaj.org/article/599d93ea3e394e98ac54e6fc38c65ecc","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 4, p 313 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2020-08-28-313","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-08-28-313","pdf_url":"https://quantum-journal.org/papers/q-2020-08-28-313/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1252004527","display_name":null,"funder_award_id":"639.022.519","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G3462424673","display_name":null,"funder_award_id":"VIDI_grant","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6763489479","display_name":null,"funder_award_id":"VI.Veni.192.159","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G7758152977","display_name":null,"funder_award_id":"support","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2985317169.pdf","grobid_xml":"https://content.openalex.org/works/W2985317169.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1848366941","https://openalex.org/W1972704456","https://openalex.org/W1975313455","https://openalex.org/W1980744208","https://openalex.org/W1989397443","https://openalex.org/W1994811895","https://openalex.org/W2011323240","https://openalex.org/W2020582875","https://openalex.org/W2098611377","https://openalex.org/W2124875584","https://openalex.org/W2146720213","https://openalex.org/W2154588779","https://openalex.org/W2160860151","https://openalex.org/W2192515608","https://openalex.org/W2290336547","https://openalex.org/W2336874127","https://openalex.org/W2346973747","https://openalex.org/W2533499557","https://openalex.org/W2884636613","https://openalex.org/W2990431562"],"related_works":[],"abstract_inverted_index":{"Unitary":[0],"<mml:math":[1,29,44,58,65,67],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi></mml:math>-designs":[2],"are":[3],"the":[4,70,93,100,106],"bread":[5],"and":[6,12,97],"butter":[7],"of":[8,21,26,85,109],"quantum":[9,87,101,115],"information":[10],"theory":[11],"beyond.":[13],"An":[14],"important":[15],"issue":[16],"in":[17,74],"practice":[18],"is":[19,72],"that":[20,42,90],"efficiently":[22],"constructing":[23],"good":[24],"approximations":[25],"such":[27],"unitary":[28],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi></mml:math>-designs.":[30],"Building":[31],"on":[32],"results":[33],"by":[34],"Aubrun":[35],"(Comm.":[36],"Math.":[37],"Phys.":[38],"2009),":[39],"we":[40,80],"prove":[41],"sampling":[43],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:msup><mml:mrow":[45],"class=\"MJX-TeXAtom-ORD\"><mml:mi":[46],"mathvariant=\"normal\">p</mml:mi><mml:mi":[47],"mathvariant=\"normal\">o</mml:mi><mml:mi":[48],"mathvariant=\"normal\">l</mml:mi><mml:mi":[49],"mathvariant=\"normal\">y</mml:mi></mml:mrow><mml:mo":[50],"stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>log</mml:mi><mml:mo>\u2061</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mrow":[51],"class=\"MJX-TeXAtom-ORD\"><mml:mo>/</mml:mo></mml:mrow><mml:mi>\u03f5</mml:mi><mml:mo":[52],"stretchy=\"false\">)</mml:mo></mml:math>":[53],"unitaries":[54],"from":[55],"an":[56,64,78],"exact":[57],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi></mml:math>-design":[59],"provides":[60],"with":[61],"positive":[62],"probability":[63],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03f5</mml:mi></mml:math>-approximate":[66],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi></mml:math>-design,":[68],"if":[69],"error":[71],"measured":[73],"one-to-one":[75],"norm.":[76],"As":[77],"application,":[79],"give":[81],"a":[82,86],"randomized":[83],"construction":[84],"encryption":[88],"scheme":[89],"has":[91],"roughly":[92],"same":[94],"key":[95],"size":[96],"security":[98],"as":[99],"one-time":[102],"pad,":[103],"but":[104],"possesses":[105],"additional":[107],"property":[108],"being":[110],"non-malleable":[111],"against":[112],"adversaries":[113],"without":[114],"side":[116],"information.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2019-11-22T00:00:00"}